The partonic process \(qg\rightarrow q\gamma \gamma \)  specified in eq. (REF ) can similarly be expressed in terms of three independent helicities, and the remaining helicities can be obtained by conjugation and/or permutation of external legs. Unlike the \(q\bar{q}\)  initiated process, however, the \(qg\)  one involves crossings between the initial and the final states. Such crossings involve a practical complication related to the nature of the pentagon functions [1]} used to express these amplitudes; it originates in the fact that these functions' representation does not allow crossings between the initial and final states in the course of their numerical evaluation. For this reason, we have computed analytically six helicities from which all remaining ones can be obtained by crossing final-state momenta only:
\(&& \mathcal {F}^{qg,\lbrace +-+--\rbrace } \quad , \quad \mathcal {F}^{qg,\lbrace ++++-\rbrace } \quad \text{and} \quad \mathcal {F}^{qg,\lbrace +++--\rbrace }\,,\nonumber \\&& \mathcal {F}^{qg,\lbrace +-++-\rbrace } \quad , \quad \mathcal {F}^{qg,\lbrace +++++\rbrace } \quad \text{and} \quad \mathcal {F}^{qg,\lbrace +-+++\rbrace }\,.\) 
